= Fourier extension estimate
{c}
{title2=$\|E_\sigma f\|_{L^q(\mathbb R^n)}\lesssim\|f\|_{L^p(\sigma)}$}
An extension estimate is a <norm> bound for the <Fourier extension operator>, uniform over its input. The exponents encode the curvature and scale of the frequency surface. For normalized circle measure, a cap of angular width $\delta$ produces size comparable to $\delta$ on a rectangle of dimensions $\delta^{-2}\times\delta^{-1}$. This single-cap example forces $p\ge4$ for a finite diagonal estimate with the same exponent $p$ on both sides.
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